MannyLazanakis Flarum should run, but you need to have SSH Access. You can run Flarum in a a subdirectory (https://yoursite.com/my-awesome-forum), or a subdomain (https://forum.yoursite.com).
One other thing to take not of, is, that Flarum is not recommended for production use. I completely disobeyed this, and ran Flarum on my production site. You can try it, but it isn't recommended.
Also, when Flarum Beta 8 comes out, most extensions will probably break. If you want to give Flarum a try anyway, use the following command:
composer create-project flarum/flarum . --stability=beta
Ensure that the directory you are installing to is totally empty, otherwise composer will throw an error.